{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multicomponent Enrichment\n",
    "\n",
    "This demonstrates how the total normalized flowrate $L_t/F$ in \n",
    "a matched abundance ratio enrichment cascade changes as a function \n",
    "of the key mass $M^*$, an optimization parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "matplotlib.rc('font', family='serif', size=16)\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from pyne import enrichment as enr\n",
    "\n",
    "NPOINTS = 50\n",
    "duc = enr.default_uranium_cascade()\n",
    "mstars = np.linspace(235.1, 237.9, NPOINTS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "calc took 2.12 ms.\n"
     ]
    }
   ],
   "source": [
    "start = time.time()\n",
    "flowrates = []\n",
    "for mstar in mstars:\n",
    "    duc.Mstar = mstar\n",
    "    casc = enr.solve_symbolic(duc)\n",
    "    flowrates.append(casc.l_t_per_feed)\n",
    "print(\"calc took {0:.3g} ms.\".format((time.time()-start) * 1e3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(10,6))\n",
    "plt.plot(mstars, flowrates, 'r-o', label='$L_t/F$')\n",
    "plt.xlabel('$M^*$ [amu]')\n",
    "plt.ylabel('Total per Feed Flow Rate [unitless]')\n",
    "lgd = plt.legend(loc=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
